The Summation of Random Causes as the Source of Cyclic Processes

ALMOST ALL of the phenomena of economic life, like many other processes, social, meteorological, and others, occur in sequences of rising and falling movements, like waves. Just as waves following each other on the sea do not repeat each other perfectly, so economic cycles never repeat earlier ones exactly either in duration or in amplitude. Nevertheless, in both cases, it is almost always possible to detect, even in the multitude of individual peculiarities of the phenomena, marks of certain approximate uniformities and regularities. The eye of the observer instinctively discovers on waves of a certain order other smaller waves, so that the idea of harmonic analysis, viz., that of the possibility of expressing the irregularities of the form and the spacing of the waves by means of the summation of regular sinusoidal fluctuations, presents itself to the mind almost spontaneously. If the results of the analysis happen sometimes not to be completely satisfactory, the discrepancies usually will be interpreted as casual deviations superposed on the regular waves. If the analyses of the first and of the second halves of a series give considerably divergent results (such as, for example, were found by Schuster while analyzing sunspot periodicity),' it is, even then, possible to find the solution without giving up the basic concept. Such a discrepancy may be the result of the interference of certain factors checking the continuous movement of the process and substituting for the former regularity a new one which sometimes may